You’ll need to set a bootable OS installer USB thumb drive so you can properly update your Mac mini. Here’s how: [https://www.macworld.com/article/3284378/how-to-create-a-bootable-macos-mojave-installer-drive.html|How to create a bootable macOS Mojave installer drive]
You have two issues the first is your iMac updated the drive to APFS on you, yet your Mini has no knowledge how to boot up under it as the systems firmware was not updated. Upgrading the system from your installer drive should fix things.